Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 3x - 9$ and $ KL = 5x - 17$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {3x - 9} = {5x - 17}$ Solve for $x$ $ -2x = -8$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 3({4}) - 9$ $ KL = 5({4}) - 17$ $ JK = 12 - 9$ $ KL = 20 - 17$ $ JK = 3$ $ KL = 3$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {3} + {3}$ $ JL = 6$